difficult question - need help

every year danielle sells 29720 cases of her cookie mix. it costs $1 per year to store a case plus annual warehouse fees of $2 per case for the maximum number of cases she will store. if it costs her $743 to set up a production run, plus $10 per case to
manufacture a single case, how many production runs will minimize cost?

For a single run the cost is $387,103 (743 + 13*29,720). However, this cost will decrease as we increase the number of runs to a certain point. This is primarily due to the lowered cost of holding less at any given time. Our costs will increase after a certain
point due to the $743 charge to set up a production run each time.

The cost to produce in two separate production runs decreased $28,977. This should continue to the point where we can minimize costs. Instead of trial and error, we can determine the first derivative of our cost function in terms of n and set it equal to
zero.